However, it is not always so easy to solve for inverses by inspection. The surefire way to do this is to use linear algebra, as I will demonstrate.
You want (we only go up to the second degree since )
Expanding the left hand side gives
So we want to find such that . Although it is obvious what the solution is in this case, I'll write down the general way to do it:
With respect to the basis , this is equivalent to solving the linear system
Which has solutions . Hence the inverse is , which is the same answer as we got from inspection.